1. Field of the Invention
The present invention relates to arithmetic apparatus in general and to an apparatus for providing a summation of the products of a predetermined number of successive pairs of numbers in particular.
2. Related Application
The present application is related to a copending application Ser. No. 655,482, filed by the applicant on Sept. 27, 1984, entitled Floating Point Add/Subtract and Multiplying Assemblies Sharing Common Normalization, Rounding and Exponential Apparatus, and assigned to the assignee of the present application. The relationship between this and the above application is that the fully combinatorial arithmetic apparatus used for adding and multiplying numbers which is disclosed in the above application is preferably, though not necessarily, used in a preferred embodiment of the present invention.
3. Description of Prior Art
A summation of the products of successive pairs of numbers is given by the following general mathematic expression: EQU .SIGMA.A.sub.i X.sub.i =A.sub.0 X.sub.0 +A.sub.1 X.sub.1 . . . A.sub.k X.sub.k
where k is a predetermined integer.
In general, the above described mathematical expression is solved by successive multiplications and a summation of the resulting products.
Heretofore, methods and apparatus for providing a summation of products resulting from a plurality of successive multiplications have required separate assemblies to perform the multiplication and summing operations. For example, it has been the practice to provide a multiplier and an adder. The multiplier was provided with a pair of inputs for receiving a pair of numbers to be multiplied and an output for providing the resulting product. The adder was provided with a pair of inputs, an output and an accumulator register having an input and an output. The output of the multiplier was coupled to one of the adder inputs, the input of the register was coupled to the output of the adder and the output of the register was coupled to the other of the adder inputs.
In use, a pair of numbers to be multiplied was applied to the multiplier inputs and the resulting product appearing on the output of the multiplier was applied to one of the inputs of the adder. A second input to the adder was obtained from the output of the accumulator register. The adder then added its inputs and the sum thereof was stored in the accumulated register for use in the next addition operation.
In general, the prior known arithmetic apparatus capable of successive multiplication and addition, such as described above, required the result of the multiplication to be re-entered externally for addition or has dedicated circuit connections limiting its use to the multiplication and summing operations as distinguished from a general purpose apparatus with a wholly internal facility for performing the stated operations.